Chapter 27:
CIRCUITS
1. “The sum of the currents into a junction equals the sum of the currents out of the junction” is
a consequence of:
A. Newton’s third law
B. Ohm’s law
C. Newton’s second law
D. conservation of energy
E. conservation of charge
ans: E
2. “The sum of the emf’s and potential differences around a closed loop equals zero” is a consequence of:
A. Newton’s third law
B. Ohm’s law
C. Newton’s second law
D. conservation of energy
E. conservation of charge
ans: D
3. A portion of a circuit is shown, with the values of the currents given for some branches. What
is the direction and value of the current i?
↑2 A
→
5A
A.
B.
C.
D.
E.
↓4 A
i
↑3 A
↑2 A
↓, 6 A
↑, 6 A
↓, 4 A
↑, 4 A
↓, 2 A
ans: A
4. Four wires meet at a junction. The first carries 4 A into the junction, the second carries 5 A
out of the junction, and the third carries 2 A out of the junction. The fourth carries:
A. 7 A out of the junction
B. 7 A into the junction
C. 3 A out of the junction
D. 3 A into the junction
E. 1 A into the junction
ans: D
Chapter 27:
CIRCUITS
387
5. In the context of the loop and junctions rules for electrical circuits a junction is:
A. where a wire is connected to a resistor
B. where a wire is connected to a battery
C. where only two wires are joined
D. where three or more wires are joined
E. where a wire is bent
ans: D
6. For any circuit the number of independent equations containing emf’s, resistances, and currents
equals:
A. the number of junctions
B. the number of junctions minus 1
C. the number of branches
D. the number of branches minus 1
E. the number of closed loops
ans: C
7. If a circuit has L closed loops, B branches, and J junctions the number of independent loop
equations is:
A. B − J + 1
B. B − J
C. B
D. L
E. L − J
ans: A
8. A battery is connected across a series combination of two identical resistors. If the potential
difference across the terminals is V and the current in the battery is i, then:
A. the potential difference across each resistor is V and the current in each resistor is i
B. the potential difference across each resistor is V /2 and the current in each resistor is i/2
C. the potential difference across each resistor is V and the current in each resistor is i/2
D. the potential difference across each resistor is V /2 and the current in each resistor is i
E. none of the above are true
ans: D
9. A battery is connected across a parallel combination of two identical resistors. If the potential
difference across the terminals is V and the current in the battery is i, then:
A. the potential difference across each resistor is V and the current in each resistor is i
B. the potential difference across each resistor is V /2 and the current in each resistor is i/2
C. the potential difference across each resistor is V and the current in each resistor is i/2
D. the potential difference across each resistor is V /2 and the current in each resistor is i
E. none of the above are true
ans: C
388
Chapter 27:
CIRCUITS
10. A total resistance of 3.0 Ω is to be produced by combining an unknown resistor R with a 12 Ω
resistor. What is the value of R and how is it to be connected to the 12 Ω resistor?
A. 4.0 Ω, parallel
B. 4.0 Ω, series
C. 2.4 Ω, parallel
D. 2.4 Ω, series
E. 9.0 Ω, series
ans: A
11. By using only two resistors, R1 and R2 , a student is able to obtain resistances of 3 Ω, 4 Ω, 12 Ω,
and 16 Ω. The values of R1 and R2 (in ohms) are:
A. 3, 4
B. 2, 12
C. 3, 16
D. 4, 12
E. 4, 16
ans: D
12. Four 20-Ω resistors are connected in parallel and the combination is connected to a 20-V emf
device. The current in the device is:
A. 0.25 A
B. 1.0 A
C. 4.0 A
D. 5.0 A
E. 100 A
ans: C
13. Four 20-Ω resistors are connected in parallel and the combination is connected to a 20-V emf
device. The current in any one of the resistors is:
A. 0.25 A
B. 1.0 A
C. 4.0 A
D. 5.0 A
E. 100 A
ans: B
14. Four 20-Ω resistors are connected in series and the combination is connected to a 20-V emf
device. The current in any one of the resistors is:
A. 0.25 A
B. 1.0 A
C. 4.0 A
D. 5.0 A
E. 100 A
ans: A
Chapter 27:
CIRCUITS
389
15. Four 20-Ω resistors are connected in series and the combination is connected to a 20-V emf
device. The potential difference across any one of the resistors is:
A. 1 V
B. 4 V
C. 5 V
D. 20 V
E. 80 V
ans: C
16. Nine identical wires, each of diameter d and length L, are connected in parallel. The combination has the same resistance as a single similar wire of length L but whose diameter is:
A. 3d
B. 9d
C. d/3
D. d/9
E. d/81
ans: A
17. Nine identical wires, each of diameter d and length L, are connected in series. The combination
has the same resistance as a single similar wire of length L but whose diameter is:
A. 3d
B. 9d
C. d/3
D. d/9
E. d/81
ans: C
18. Two wires made of the same material have the same lengths but different diameters. They are
connected in parallel to a battery. The quantity that is NOT the same for the wires is:
A. the end-to-end potential difference
B. the current
C. the current density
D. the electric field
E. the electron drift velocity
ans: B
19. Two wires made of the same material have the same lengths but different diameters. They are
connected in series to a battery. The quantity that is the same for the wires is:
A. the end-to-end potential difference
B. the current
C. the current density
D. the electric field
E. the electron drift velocity
ans: B
390
Chapter 27:
CIRCUITS
20. The equivalent resistance between points 1 and 2 of the circuit shown is:
1Ω
1Ω
. . .
.........................
. . .
. . .
.........................
. . .
•1
...........................
. . .
...........................
. . .
2Ω
2Ω
•2
..........
..
............
..
............
....
..........
.
......
1 Ω .........................
A.
B.
C.
D.
E.
4Ω
3Ω
4Ω
5Ω
6Ω
7Ω
ans: C
21. Each of the resistors in the diagram has a resistance of 12 Ω. The resistance of the entire circuit
is:
. . .
......................
. . .
. . .
......................
. . .
. . .
.........................
. . .
•
. . .
.........................
. . .
. . .
.........................
. . .
A.
B.
C.
D.
E.
•
•
. . .
.........................
. . .
. . .
.........................
. . .
•
•
. . .
.........................
. . .
•
. . .
.........................
. . .
•
. . .
.........................
. . .
5.76 Ω
25 Ω
48 Ω
120 Ω
none of these
ans: B
22. The resistance of resistor 1 is twice the resistance of resistor 2. The two are connected in
parallel and a potential difference is maintained across the combination. Then:
A. the current in 1 is twice that in 2
B. the current in 1 is half that in 2
C. the potential difference across 1 is twice that across 2
D. the potential difference across 1 is half that across 2
E. none of the above are true
ans: B
Chapter 27:
CIRCUITS
391
23. The resistance of resistor 1 is twice the resistance of resistor 2. The two are connected in series
and a potential difference is maintained across the combination. Then:
A. the current in 1 is twice that in 2
B. the current in 1 is half that in 2
C. the potential difference across 1 is twice that across 2
D. the potential difference across 1 is half that across 2
E. none of the above are true
ans: C
24. Resistor 1 has twice the resistance of resistor 2. The two are connected in series and a potential
difference is maintained across the combination. The rate of thermal energy generation in 1 is:
A. the same as that in 2
B. twice that in 2
C. half that in 2
D. four times that in 2
E. one-fourth that in 2
ans: B
25. Resistor 1 has twice the resistance of resistor 2. The two are connected in parallel and a potential difference is maintained across the combination. The rate of thermal energy generation
in 1 is:
A. the same as that in 2
B. twice that in 2
C. half that in 2
D. four times that in 2
E. one-fourth that in 2
ans: C
26. The emf of a battery is equal to its terminal potential difference:
A. under all conditions
B. only when the battery is being charged
C. only when a large current is in the battery
D. only when there is no current in the battery
E. under no conditions
ans: D
27. The terminal potential difference of a battery is less than its emf:
A. under all conditions
B. only when the battery is being charged
C. only when the battery is being discharged
D. only when there is no current in the battery
E. under no conditions
ans: C
392
Chapter 27:
CIRCUITS
28. A battery has an emf of 9 V and an internal resistance of 2 Ω. If the potential difference across
its terminals is greater than 9 V:
A. it must be connected across a large external resistance
B. it must be connected across a small external resistance
C. the current must be out of the positive terminal
D. the current must be out of the negative terminal
E. the current must be zero
ans: D
29. A battery with an emf of 24 V is connected to a 6-Ω resistor. As a result, current of 3 A exists
in the resistor. The terminal potential difference of the battery is:
A. 0
B. 6 V
C. 12 V
D. 18 V
E. 24 V
ans: D
30. In the diagram R1 > R2 > R3 . Rank the three resistors according to the current in them, least
to greatest.
R1
.. .. ..
............................
. . .
..........
......
............
......
............
..
.....
E
R2
.. .. ..
............................
. . .
R3
A.
B.
C.
D.
E.
1, 2, 3
3, 2, 1
1, 3, 2
3, 1, 3
All are the same
ans: E
31. Resistances of 2.0 Ω, 4.0 Ω, and 6.0 Ω and a 24-V emf device are all in parallel. The current in
the 2.0-Ω resistor is:
A. 12 A
B. 4.0 A
C. 2.4 A
D. 2.0 A
E. 0.50 A
ans: A
Chapter 27:
CIRCUITS
393
32. Resistances of 2.0 Ω, 4.0 Ω, and 6.0 Ω and a 24-V emf device are all in series. The potential
difference across the 2.0-Ω resistor is:
A. 4 V
B. 8 V
C. 12 V
D. 24 V
E. 48 V
ans: A
33. A battery with an emf of 12 V and an internal resistance of 1 Ω is used to charge a battery with
an emf of 10 V and an internal resistance of 1 Ω. The current in the circuit is:
A. 1 A
B. 2 A
C. 4 A
D. 11 A
E. 22 A
ans: A
34. In the diagram, the current in the 3-Ω resistor is 4 A. The potential difference between points
1 and 2 is:
3Ω
A.
B.
C.
D.
E.
2Ω
.. .. ..
.........................
.. .. ..
1•
.. .. ..
.........................
.. .. ..
•2
0.75 V
0.8 V
1.25 V
12 V
20 V
ans: E
35. The current in the 5.0-Ω resistor in the circuit shown is:
. . .
.........................
6.0 Ω
12 V
A.
B.
C.
D.
E.
394
0.42 A
0.67 A
1.5 A
2.4 A
3.0 A
ans: C
Chapter 27:
CIRCUITS
. .
............................
...............................
4.0 Ω
12 Ω
. . .
.........................
. . .
.........................
3.0 Ω
5.0 Ω
36. A 3-Ω and a 1.5-Ω resistor are wired in parallel and the combination is wired in series to a 4-Ω
resistor and a 10-V emf device. The current in the 3-Ω resistor is:
A. 0.33 A
B. 0.67 A
C. 2.0 A
D. 3.3 A
E. 6.7 A
ans: B
37. A 3-Ω and a 1.5-Ω resistor are wired in parallel and the combination is wired in series to a 4-Ω
resistor and a 10-V emf device. The potential difference across the 3-Ω resistor is:
A. 2.0 V
B. 6.0 V
C. 8.0 V
D. 10 V
E. 12 V
ans: A
38. Two identical batteries, each with an emf of 18 V and an internal resistance of 1 Ω, are wired in
parallel by connecting their positive terminals together and connecting their negative terminals
together. The combination is then wired across a 4-Ω resistor. The current in the 4-Ω resistor
is:
A. 1.0 A
B. 2.0 A
C. 4.0 A
D. 3.6 A
E. 7.2 A
ans: C
39. Two identical batteries, each with an emf of 18 V and an internal resistance of 1 Ω, are wired in
parallel by connecting their positive terminals together and connecting their negative terminals
together. The combination is then wired across a 4-Ω resistor. The current in each battery is:
A. 1.0 A
B. 2.0 A
C. 4.0 A
D. 3.6 A
E. 7.2 A
ans: B
Chapter 27:
CIRCUITS
395
40. Two identical batteries, each with an emf of 18 V and an internal resistance of 1 Ω, are wired in
parallel by connecting their positive terminals together and connecting their negative terminals
together. The combination is then wired across a 4-Ω resistor. The potential difference across
the 4-Ω resistor is:
A. 4.0 V
B. 8.0 V
C. 14 V
D. 16 V
E. 29 V
ans: D
41. In the diagrams, all light bulbs are identical and all emf devices are identical. In which circuit
(A, B, C, D, E) will the bulbs glow with the same brightness as in circuit X?
....
.......................
..... ................... ....
... .. ......
................
.. ..
............
...................
..... ................ ....
....... .......
.............
.. .
....
.......................
..... ................... ....
... .. ......
................
.. ..
A
...
....
...
...................... ...................... ......................
..... .................... .... ..... .................... .... ..... .................... ....
... .. .. .... ... .. .. .... ... .. .. ....
................. ................. .................
. .
. ..
. ..
....
.......................
..... ................... ...
... .. .. ....
.................
.. ..
B
C
•
..........
..........................
..... ................ ...
.........................
..........
..........
..........................
..... ................ ...
.........................
..........
•
•
...........
...................
..... .................. ....
... ... ... ...
...............
. .
•
D
X
...........
........................
..... ................. ...
........................
.............
...........
...................
..... .................. ....
... ... ... ...
...............
. .
E
ans: D
42. In the diagrams, all light bulbs are identical and all emf devices are identical. In which circuit
(A, B, C, D, E) will the bulbs be dimmest?
..........
...............
.... .................... ...
... ... .......
..............
.. ..
.............. .............. ..............
... ........... ... ... ........... ... ... ........... ...
.... ................. .... .... ................ .... .... ................ ....
....... ... ... ....... ... ... ....... ... ...
............. .............. ..............
. .
. .
. .
..........
...............
.... .................... ...
... ... .......
..............
.. ..
A
•
..............
... ........... ...
.... ................. ....
....... ........
.............
. .
............
...................
.... ................. ....
....... .......
..............
. .
C
ans: D
396
Chapter 27:
CIRCUITS
•
B
•
•
..........
................
.... .................... ....
... ... ... ...
.............
.. ..
..........
................
.... .................... ....
... ... ... ...
.............
.. ..
D
•
..........
................
.... .................... ....
... ... ... ...
.............
.. ..
......
...................
..... ................. ...
... ... . ... ....
.................
.. ..
E
•
43. A 120-V power line is protected by a 15-A fuse. What is the maximum number of “120 V,
500 W” light bulbs that can be operated at full brightness from this line?
A. 1
B. 2
C. 3
D. 4
E. 5
ans: C
44. Two 110-V light bulbs, one “25 W” and the other “100 W”, are connected in series to a 110 V
source. Then:
A. the current in the 100-W bulb is greater than that in the 25-W bulb
B. the current in the 100-W bulb is less than that in the 25-W bulb
C. both bulbs will light with equal brightness
D. each bulb will have a potential difference of 55 V
E. none of the above
ans: E
45. A resistor with resistance R1 and a resistor with resistance R2 are connected in parallel to an
ideal battery with emf E. The rate of thermal energy generation in the resistor with resistance
R1 is:
A. E 2 /R1
B. E 2 R1 /(R1 + R2 )2
C. E 2 /(R1 + R2 )
D. E 2 /R2
E. E 2 R1 /R22
ans: A
46. In an antique automobile, a 6-V battery supplies a total of 48 W to two identical headlights in
parallel. The resistance (in ohms) of each bulb is:
A. 0.67
B. 1.5
C. 3
D. 4
E. 8
ans: B
47. Resistor 1 has twice the resistance of resistor 2. They are connected in parallel to a battery.
The ratio of the thermal energy generation rate in 1 to that in 2 is:
A. 1 : 4
B. 1 : 2
C. 1 : 1
D. 2 : 1
E. 4 : 1
ans: B
Chapter 27:
CIRCUITS
397
48. A series circuit consists of a battery with internal resistance r and an external resistor R. If
these two resistances are equal (r = R) then the thermal energy generated per unit time by
the internal resistance r is:
A. the same as by R
B. half that by R
C. twice that by R
D. one-third that by R
E. unknown unless the emf is given
ans: A
49. The positive terminals of two batteries with emf’s of E1 and E2 , respectively, are connected
together. Here E2 > E1 . The circuit is completed by connecting the negative terminals. If
each battery has an internal resistance r, the rate with which electrical energy is converted to
chemical energy in the smaller battery is:
A. E12 /r
B. E12 /2r
C. (E2 − E1 )E1 /r
D. (E2 − E1 )E1 /2r
E. E22 /2r
ans: D
50. In the figure, voltmeter V1 reads 600 V, voltmeter V2 reads 580 V, and ammeter A reads 100 A.
The power wasted in the transmission line connecting the power house to the consumer is:
power
house
•
398
1 kW
2 kW
58 kW
59 kW
60 kW
ans: B
Chapter 27:
CIRCUITS
A
......
...... ........
...
..
....
..
.... 1.....
...............
V
•
A.
B.
C.
D.
E.
.................
....
..
..
.....
...
..
...... .......
.......
......
...... ........
...
..
....
..
.... 2.....
...............
V
transmission line
•
consumer
•
51. The circuit shown was wired for the purpose of measuring the resistance of the lamp L. Inspection shows that:
..
..........
.......
...
.
.
...... ....... .......
.
. ... ... ... ... ... ...
..... ..... .....
•
R
...................
...
...
....
.
...
..
...... .......
.......
L
•
...................
...
...
.....
.
...
..
...... .......
........
•
...................
...
...
....
.
...
..
...... .......
.......
A
to 120 V
A.
B.
C.
D.
E.
•
V
voltmeter V and rheostat R should be interchanged
the circuit is satisfactory
the ammeter A should be in parallel with R, not L
the meters, V and A, should be interchanged
L and V should be interchanged
ans: D
52. When switch S is open, the ammeter in the circuit shown reads 2.0 A. When S is closed, the
ammeter reading:
15 Ω
.. .. ..
.........................
.. .. ..
•
...................
...
..
.
.....
...
...
...... .........
.....
A
20 Ω
...........
.....
............
......
............
..
......
...........
.....
............
.....
............
..
......
60 Ω
• ...........
..
....
S
•
A.
B.
C.
D.
E.
increases slightly
remains the same
decreases slightly
doubles
halves
ans: A
53. A certain galvanometer has a resistance of 100 Ω and requires 1 mA for full scale deflection. To
make this into a voltmeter reading 1 V full scale, connect a resistance of:
A. 1000 Ω in parallel
B. 900 Ω in series
C. 1000 Ω in series
D. 10 Ω in parallel
E. 0.1 Ω in series
ans: B
Chapter 27:
CIRCUITS
399
54. To
A.
B.
C.
D.
E.
make a galvanometer into an ammeter, connect:
a high resistance in parallel
a high resistance in series
a low resistance in series
a low resistance in parallel
a source of emf in series
ans: D
55. A certain voltmeter has an internal resistance of 10, 000 Ω and a range from 0 to 100 V. To
give it a range from 0 to 1000 V, one should connect:
A. 100, 000 Ω in series
B. 100, 000 Ω in parallel
C. 1000 Ω in series
D. 1000 Ω in parallel
E. 90, 000 Ω in series
ans: E
56. A certain ammeter has an internal resistance of 1 Ω and a range from 0 to 50 mA. To make its
range from 0 to 5 A, use:
A. a series resistance of 99 Ω
B. an extremely large (say 106 Ω ) series resistance
C. a resistance of 99 Ω in parallel
D. a resistance of 1/99 Ω in parallel
E. a resistance of 1/1000 Ω in parallel
ans: D
57. A galvanometer has an internal resistance of 12 Ω and requires 0.01 A for full scale deflection.
To convert it to a voltmeter reading 3 V full scale, one must use a series resistance of:
A. 102 Ω
B. 288 Ω
C. 300 Ω
D. 360 Ω
E. 412 Ω
ans: B
58. A certain voltmeter has an internal resistance of 10, 000 Ω and a range from 0 to 12 V. To
extend its range to 120 V, use a series resistance of:
A. 1, 111 Ω
B. 90, 000 Ω
C. 100, 000 Ω
D. 108, 000 Ω
E. 120, 000 Ω
ans: B
400
Chapter 27:
CIRCUITS
59. Four circuits have the form shown in the diagram. The capacitor is initially uncharged and the
switch S is open.
S
• •
....
....
....
....
.
R
... ... ...
.. ....... ....... ......
.. .. ..
E
C
The values of the emf E, resistance R, and capacitance C for each of the circuits are
circuit 1: E = 18 V, R = 3 Ω, C = 1 µF
circuit 2: E = 18 V, R = 6 Ω, C = 9 µF
circuit 3: E = 12 V, R = 1 Ω, C = 7 µF
circuit 4: E = 10 V, R = 5 Ω, C = 7 µF
Rank the circuits according to the current just after switch S is closed least to greatest.
A. 1, 2, 3, 4
B. 4, 3, 2, 1
C. 4, 2, 3, 1
D. 4, 2, 1, 3
E. 3, 1, 2, 4
ans: D
60. Four circuits have the form shown in the diagram. The capacitor is initially uncharged and the
switch S is open.
S
• •
....
....
....
....
.
E
R
.. .. ..
.........................
.. .. ..
C
The values of the emf E, resistance R, and capacitance C for each of the circuits are
circuit 1: E = 18 V, R = 3 Ω, C = 1 µF
circuit 2: E = 18 V, R = 6 Ω, C = 9 µF
circuit 3: E = 12 V, R = 1 Ω, C = 7 µF
circuit 4: E = 10 V, R = 5 Ω, C = 7 µF
Rank the circuits according to the time after switch S is closed for the capacitors to reach half
their final charges, least to greatest.
A. 1, 2, 3, 4
B. 4, 3, 2, 1
C. 1, 3, 4, 2
D. 1 and 2 tied, then 4, 3
E. 4, 3, then 1 and 2 tied
ans: C
Chapter 27:
CIRCUITS
401
61. The time constant RC has units of:
A. second/farad
B. second/ohm
C. 1/second
D. second/watt
E. none of these
ans: E
62. In the circuit shown, both resistors have the same value R. Suppose switch S is initially closed.
When it is then opened, the circuit has a time constant τa . Conversely, suppose S is initially
open. When it is then closed, the circuit has a time constant τb . The ratio τa /τb is:
. . .
.........................
•
R
C
R
.
.....
......
......
S
..........
..
............
.
............
.....
E
•
A.
B.
C.
D.
E.
1
2
0.5
0.667
1.5
ans: B
63. In the circuit shown, the capacitor is initially uncharged. At time t = 0, switch S is closed. If
τ denotes the time constant, the approximate current through the 3 Ω resistor when t = τ /10
is:
. . .
.........................
. . .
•
S •
6Ω
....
....
....
....
.
10 V
A.
B.
C.
D.
E.
402
0.38 A
0.50 A
0.75 A
1.0 A
1.5 A
ans: D
Chapter 27:
CIRCUITS
6 µF
..........
..
............
..
............
.....
3Ω
64. Suppose the current charging a capacitor is kept constant. Which graph below correctly gives
the potential difference V across the capacitor as a function of time?
V
.............
.....
.
.
.
...
...
.
.
.
..
.. .
V
V
...........................................
t
t
A
....
.....
.
.
.
....
.....
.
.
...
....
.
.
.
..
B
V
.
..
.
..
...
.
.
..
....
.
.
.
.
.............
D
C
V
t
t
..
..
..
..
..
..
..
t
E
ans: C
65. A charged capacitor is being discharged through a resistor. At the end of one time constant
the charge has been reduced by (1 − 1/e) = 63% of its initial value. At the end of two time
constants the charge has been reduced by what percent of its initial value?
A. 82%
B. 86%
C. 100%
D. Between 90% and 100%
E. Need to know more data to answer the question
ans: B
66. An initially uncharged capacitor C is connected in series with resistor R. This combination is
then connected to a battery of emf V0 . Sufficient time elapses so that a steady state is reached.
Which of the following statements is NOT true?
A. The time constant is independent of V0
B. The final charge on C is independent of R
C. The total thermal energy generated by R is independent of R
D. The total thermal energy generated by R is independent of V0
E. The initial current (just after the battery was connected) is independent of C
ans: C
67. A certain capacitor, in series with a resistor, is being charged. At the end of 10 ms its charge
is half the final value. The time constant for the process is about:
A. 0.43 ms
B. 2.3 ms
C. 6.9 ms
D. 10 ms
E. 14 ms
ans: E
Chapter 27:
CIRCUITS
403
68. A certain capacitor, in series with a 720-Ω resistor, is being charged. At the end of 10 ms its
charge is half the final value. The capacitance is about:
A. 9.6 µF
B. 14 µF
C. 20 µF
D. 7.2 F
E. 10 F
ans: C
69. In the capacitor discharge formula q = q0 e−t/RC the symbol t represents:
A. the time constant
B. the time it takes for C to lose the fraction 1/e of its initial charge
C. the time it takes for C to lose the fraction (1 − 1/e) of its initial charge
D. the time it takes for C to lose essentially all of its initial charge
E. none of the above
ans: E
404
Chapter 27:
CIRCUITS
Chapter 28:
MAGNETIC FIELDS
1. Units of a magnetic field might be:
A. C·m/s
B. C·s/m
C. C/kg
D. kg/C·s
E. N/C·m
ans: D
2. In the formula F = qv × B:
A. F must be perpendicular to v but not necessarily to B
B. F must be perpendicular to B but not necessarily to v
C. v must be perpendicular to B but not necessarily to F
D. all three vectors must be mutually perpendicular
E. F must be perpendicular to both v and B
ans: E
3. An electron moves in the negative x direction, through a uniform magnetic field in the negative
y direction. The magnetic force on the electron is:
y
..
...
..
...
...
...
...
.
...
...
....
...
....
...
....
... .......
... .....
..
......................................................................................................................................
.. ...
.
.
.
.. ...
.
.
.
..
....
....
....
....
....
..
...
.
.
.
...
..
.
.
....
.
..
.
.
..
.
..
.
.
.
...
....
....
..
..
v
...........................•...
...
.
........
. B
x
z
A.
B.
C.
D.
E.
4. At
A.
B.
C.
D.
E.
in the negative x direction
in the positive y direction
in the negative y direction
in the positive z direction
in the negative z direction
ans: E
any point the magnetic field lines are in the direction of:
the magnetic force on a moving positive charge
the magnetic force on a moving negative charge
the velocity of a moving positive charge
the velocity of a moving negative charge
none of the above
ans: E
Chapter 28:
MAGNETIC FIELDS
405
5. The magnetic force on a charged particle is in the direction of its velocity if:
A. it is moving in the direction of the field
B. it is moving opposite to the direction of the field
C. it is moving perpendicular to the field
D. it is moving in some other direction
E. never
ans: E
6. A magnetic field exerts a force on a charged particle:
A. always
B. never
C. if the particle is moving across the field lines
D. if the particle is moving along the field lines
E. if the particle is at rest
ans: C
7. The direction of the magnetic field in a certain region of space is determined by firing a test
charge into the region with its velocity in various directions in different trials. The field direction
is:
A. one of the directions of the velocity when the magnetic force is zero
B. the direction of the velocity when the magnetic force is a maximum
C. the direction of the magnetic force
D. perpendicular to the velocity when the magnetic force is zero
E. none of the above
ans: A
8. An electron is moving north in a region where the magnetic field is south. The magnetic force
exerted on the electron is:
A. zero
B. up
C. down
D. east
E. west
ans: A
9. A magnetic field CANNOT:
A. exert a force on a charged particle
B. change the velocity of a charged particle
C. change the momentum of a charged particle
D. change the kinetic energy of a charged particle
E. change the trajectory of a charged particle
ans: D
406
Chapter 28:
MAGNETIC FIELDS
10. A proton (charge e), traveling perpendicular to a magnetic field, experiences the same force as
an alpha particle (charge 2e) which is also traveling perpendicular to the same field. The ratio
of their speeds, vproton /valpha , is:
A. 0.5
B. 1
C. 2
D. 4
E. 8
ans: C
11. A hydrogen atom that has lost its electron is moving east in a region where the magnetic field
is directed from south to north. It will be deflected:
A. up
B. down
C. north
D. south
E. not at all
ans: A
12. A beam of electrons is sent horizontally down the axis of a tube to strike a fluorescent screen
at the end of the tube. On the way, the electrons encounter a magnetic field directed vertically
downward. The spot on the screen will therefore be deflected:
A. upward
B. downward
C. to the right as seen from the electron source
D. to the left as seen from the electron source
E. not at all
ans: C
13. An electron (charge = −1.6 × 10−19 C) is moving at 3 × 105 m/s in the positive x direction. A
magnetic field of 0.8 T is in the positive z direction. The magnetic force on the electron is:
A. 0
B. 4 × 10−14 N, in the positive z direction
C. 4 × 10−14 N, in the negative z direction
D. 4 × 10−14 N, in the positive y direction
E. 4 × 10−14 N, in the negative y direction
ans: D
14. At one instant an electron (charge = −1.6×10−19 C) is moving in the xy plane, the components
of its velocity being vx = 5 × 105 m/s and vy = 3 × 105 m/s. A magnetic field of 0.8 T is in the
positive x direction. At that instant the magnitude of the magnetic force on the electron is:
A. 0
B. 2.6 × 10−14 N
C. 3.8 × 10−14 N
D. 6.4 × 10−14 N
E. 1.0 × 10−13 N
ans: C
Chapter 28:
MAGNETIC FIELDS
407
15. At one instant an electron (charge = −1.6×10−19 C) is moving in the xy plane, the components
of its velocity being vx = 5 × 105 m/s and vy = 3 × 105 m/s. A magnetic field of 0.8 T is in the
positive x direction. At that instant the magnitude of the magnetic force on the electron is:
A. 0
B. 3.8 × 10−14 N
C. 5.1 × 10−14 N
D. 6.4 × 10−14 N
E. 7.5 × 10−14 N
ans: B
16. An electron travels due north through a vacuum in a region of uniform magnetic field B that
is also directed due north. It will:
A. be unaffected by the field
B. speed up
C. slow down
D. follow a right-handed corkscrew path
E. follow a left-handed corkscrew path
ans: A
17. At one instant an electron is moving in the positive x direction along the x axis in a region
where there is a uniform magnetic field in the positive z direction. When viewed from a point
on the positive z axis, it subsequent motion is:
A. straight ahead
B. counterclockwise around a circle in the xy plane
C. clockwise around a circle in the xy plane
D. in the positive z direction
E. in the negative z direction
ans: B
18. A uniform magnetic field is directed into the page. A charged particle, moving in the plane of
the page, follows a clockwise spiral of decreasing radius as shown. A reasonable explanation is:
⊗
⊗
⊗
⊗
.................................
.........
....... .
.......
...... ..
......
............................... ...................
....
.
.
.
.
.
.
.
.
......
..
... ..........
.... ......
.
.
.
.
...
.
.
.
.
.
.
..
.
.
.
.
.
..
..
.
.
.
.
.
.
.
.
.
.
.....
...
... ..... ....
...
...
.....
.... .... .... ................ .... .... ....
..
..
..
.
... ... ... ...
..
.
.
..
.
...
..
..
.. .... .... ....
.. .... ....
.
....
... ....
..
...
...
.
.
.
.
.
....................
.
...
.
...
.
.
.
.
.
.
..
.
... .........
..... ....
...
...............................
...
.....
.....
......
......
.
.......
.
.
.
.
.
.............................
⊗
A.
B.
C.
D.
E.
408
⊗
MAGNETIC FIELDS
•
⊗
⊗
⊗
⊗
⊗
⊗
⊗
B
⊗
the charge is positive and slowing down
the charge is negative and slowing down
the charge is positive and speeding up
the charge is negative and speeding up
none of the above
ans: B
Chapter 28:
⊗
⊗
particle
19. An electron and a proton each travel with equal speeds around circular orbits in the same
uniform magnetic field, as shown in the diagram (not to scale). The field is into the page on
the diagram. Because the electron is less massive than the proton and because the electron is
negatively charged and the proton is positively charged:
•
•
.....................
.........
......
.....
...
....
...
..
...
.
...
.....
..
...
...
...
...
..
.
.
...
.
.
...
.
.
.
.
.....
.......
.....
............................
⊗
B
..............................
...............
.........
........
.......
.......
......
......
.....
.
.
.
.
....
....
.
....
.
..
.
...
.
..
...
.
.
...
...
.
...
..
...
.
...
....
..
...
..
..
...
..
..
...
..
...
..
.
...
....
...
...
...
.
...
..
...
...
...
...
...
...
...
.
....
..
....
...
......
.....
......
......
.......
......
.
.
.
.
.
..........
.
.
..........................................
A. the electron travels clockwise around the smaller circle and the proton travels counterclockwise around the larger circle
B. the electron travels counterclockwise around the smaller circle and the proton travels clockwise around the larger circle
C. the electron travels clockwise around the larger circle and the proton travels counterclockwise around the smaller circle
D. the electron travels counterclockwise around the larger circle and the proton travels clockwise around the smaller circle
E. the electron travels counterclockwise around the smaller circle and the proton travels counterclockwise around the larger circle
ans: A
20. An electron is launched with velocity v in a uniform magnetic field B. The angle θ between
v and B is between 0 and 90◦ . As a result, the electron follows a helix, its velocity vector v
returning to its initial value in a time interval of:
A. 2πm/eB
B. 2πmv/eB
C. 2πmv sin θ/eB
D. 2πmv cos θ/eB
E. none of these
ans: A
21. An electron and a proton are both initially moving with the same speed and in the same
direction at 90◦ to the same uniform magnetic field. They experience magnetic forces, which
are initially:
A. identical
B. equal in magnitude but opposite in direction
C. in the same direction and differing in magnitude by a factor of 1840
D. in opposite directions and differing in magnitude by a factor of 1840
E. equal in magnitude but perpendicular to each other.
ans: B
Chapter 28:
MAGNETIC FIELDS
409
22. An electron enters a region of uniform perpendicular E and B fields. It is observed that the
velocity v of the electron is unaffected. A possible explanation is:
A. v is parallel to E and has magnitude E/B
B. v is parallel to B
C. v is perpendicular to both E and B and has magnitude B/E
D. v is perpendicular to both E and B and has magnitude E/B
E. the given situation is impossible
ans: D
23. A charged particle is projected into a region of uniform, parallel, E and B fields. The force on
the particle is:
A. zero
B. at some angle < 90◦ with the field lines
C. along the field lines
D. perpendicular to the field lines
E. unknown (need to know the sign of the charge)
ans: B
24. A uniform magnetic field is in the positive z direction. A positively charged particle is moving
in the positive x direction through the field. The net force on the particle can be made zero
by applying an electric field in what direction?
A. Positive y
B. Negative y
C. Positive x
D. Negative x
E. Positive z
ans: B
25. An electron is traveling in the positive x direction. A uniform electric field E is in the negative
y direction. If a uniform magnetic field with the appropriate magnitude and direction also
exists in the region, the total force on the electron will be zero. The appropriate direction for
the magnetic field is:
y
v
•..........................
.
........
.E
A.
B.
C.
D.
E.
410
the positive y direction
the negative y direction
into the page
out of the page
the negative x direction
ans: C
Chapter 28:
MAGNETIC FIELDS
x
26. An ion with a charge of +3.2×10−19 C is in a region where a uniform electric field of 5×104 V/m
is perpendicular to a uniform magnetic field of 0.8 T. If its acceleration is zero then its speed
must be:
A. 0
B. 1.6 × 104 m/s
C. 4.0 × 104 m/s
D. 6.3 × 104 m/s
E. any value but 0
ans: D
27. The current is from left to right in the conductor shown. The magnetic field is into the page
and point S is at a higher potential than point T. The charge carriers are:
S
•
.....
...........................................................................
....
i
•
T
A.
B.
C.
D.
E.
positive
negative
neutral
absent
moving near the speed of light
ans: A
28. Electrons (mass m, charge −e) are accelerated from rest through a potential difference V and
are then deflected by a magnetic field B that is perpendicular to their velocity. The radius of
the resulting electron trajectory is:
0
A. ( √2eV /m)/B
B. B0 2eV /m
C. ( √2mV /e)/B
D. B 2mV /e
E. none of these
ans: C
29. In a certain mass spectrometer, an ion beam passes through a velocity filter consisting of
mutually perpendicular fields E and B. The beam then enters a region of another magnetic
field B perpendicular to the beam. The radius of curvature of the resulting ion beam is
proportional to:
A. EB /B
B. EB/B
C. BB /E
D. B/EB
E. E/BB
ans: E
Chapter 28:
MAGNETIC FIELDS
411
30. A cyclotron operates with a given magnetic field and at a given frequency. If R denotes the
radius of the final orbit, the final particle energy is proportional to:
A. 1/R
B. R
C. R2
D. R3
E. R4
ans: C
31. J. J. Thomson’s experiment, involving the motion of an electron beam in mutually perpendicular E and B fields, gave the value of:
A. mass of an electron
B. charge of an electron
C. Earth’s magnetic field
D. charge/mass ratio for electrons
E. Avogadro’s number
ans: D
32. The diagram shows a straight wire carrying a flow of electrons into the page. The wire is
between the poles of a permanent magnet. The direction of the magnetic force exerted on the
wire is:
N
A.
B.
C.
D.
E.
412
↑
↓
←
→
into the page
ans: A
Chapter 28:
MAGNETIC FIELDS
....
...... .......
..
.....
.... .....
.........
S
33. The figure shows the motion of electrons in a wire that is near the N pole of a magnet. The
wire will be pushed:
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
•••
...
...
...
•
...
•
...
•
...
•
•
•
•
•
...
•
•
•
...
•
•
•
•
•
•
•
...
•
•
•
...
••• •••••••••••
...
...
••• ••••••• .....................
...
...
...
..
...
•
.
.
.
.
•
.
.... ......
.
.
...
...
•••
..
...
...
.......
.............. ...
...
.
...
.......
.
...
....... .........
.......
...
.
.
.
.
.
.
.
.
.
.
.
.
...
...
...
.... ...........
.
.
.
.
.
.
.
.
.
.
...
.
.
... ......
.... .............
.
.
.
...
.
...........
.
.
... ......... ..
...
...
.......
..
.
...
...... . ......
....
...
...
...................... .......
.
...
... .........................................
...
.
.
...
.
. ...... .. .......
.
.
.
.
...
.
.......
....
.
.
.
.
.
.
.
.
.
.
.
.
.
.
... ........
....
....
.
.
.
.
.
.
.
.
.
.
.........
.
.
.
..
...
.......
.......
....... ................
.......
........
...
.......
..... .... ............ .... ....
.......
... .. ............
.........
...... ........
....
A.
B.
C.
D.
E.
electron
flow
toward the magnet
away from the magnet
downwards
upwards
along its length
ans: D
34. The diagram shows a straight wire carrying current i in a uniform magnetic field. The magnetic
force on the wire is indicated by an arrow but the magnetic field is not shown. Of the following
possibilities, the direction of the magnetic field is:
i
..
.......................................................................
..
...
...
...
...
...
...
...
.
..........
.......
...
A.
B.
C.
D.
E.
F
opposite the direction of the current
opposite the direction of F
in the direction of F
into the page
out of the page
ans: E
Chapter 28:
MAGNETIC FIELDS
413
35. The figure shows a uniform magnetic field B directed to the left and a wire carrying a current
into the page. The magnetic force acting on the wire is:
....
...................................................................................................................................................................................................................
....
....
...................................................................................................................................................................................................................
....
B
i
....
...................................................................................................................................................................................................................
....
....
...................................................................................................................................................................................................................
....
A.
B.
C.
D.
E.
toward
toward
toward
toward
zero
ans: A
the
the
the
the
top of the page
bottom of the page
left
right
36. A loop of wire carrying a current of 2.0 A is in the shape of a right triangle with two equal sides,
each 15 cm long. A 0.7 T uniform magnetic field is parallel to the hypotenuse. The resultant
magnetic force on the two equal sides has a magnitude of:
A. 0
B. 0.21 N
C. 0.30 N
D. 0.41 N
E. 0.51 N
ans: A
37. A loop of wire carrying a current of 2.0 A is in the shape of a right triangle with two equal
sides, each 15 cm long. A 0.7 T uniform magnetic field is in the plane of the triangle and is
perpendicular to the hypotenuse. The magnetic force on either of the two equal sides has a
magnitude of:
A. zero
B. 0.105 N
C. 0.15 N
D. 0.21 N
E. 0.25 N
ans: C
38. A current is clockwise around the outside edge of this page and a uniform magnetic field is
directed parallel to the page, from left to right. If the magnetic force is the only force acting
on the page, the page will turn so the right edge:
A. moves toward you
B. moves away from you
C. moves to your right
D. moves to your left
E. does not move
ans: A
414
Chapter 28:
MAGNETIC FIELDS
39. A square loop of wire lies in the plane of the page and carries a current I as shown. There is a
uniform magnetic field B parallel to the side MK as indicated. The loop will tend to rotate:
R
.
.
K .......................................................................................... L
...
...
...
...
..
..
..
..
.
..
.. B ....
..
...
..
..
..
...
..
..
..
... Q
..
..
P ...
..
..
..
..
.. .........
..
....
.... I
..
..
I .....
...
..
..
..
.
..
..
..
................................................................................
.
.
M
N
.
.
S
A.
B.
C.
D.
E.
about PQ with KL coming out of the page
about PQ with KL going into the page
about RS with MK coming out of the page
about RS with MK going into the page
about an axis perpendicular to the page.
ans: A
40. The units of magnetic dipole moment are:
A. ampere
B. ampere·meter
C. ampere·meter2
D. ampere/meter
E. ampere/meter2
ans: C
41. You are facing a loop of wire which carries a clockwise current of 3.0 A and which surrounds
an area of 5.8 × 10−2 m2 . The magnetic dipole moment of the loop is:
A. 3.0 A · m2 , away from you
B. 3.0 A · m2 , toward you
C. 0.17 A · m2 , away from you
D. 0.17 A · m2 , toward you
E. 0.17 A · m2 , left to right
ans: C
42. The magnetic torque exerted on a flat current-carrying loop of wire by a uniform magnetic
field B is:
A. maximum when the plane of the loop is perpendicular to B
B. maximum when the plane of the loop is parallel to B
C. dependent on the shape of the loop for a fixed loop area
D. independent of the orientation of the loop
E. such as to rotate the loop around the magnetic field lines
ans: B
Chapter 28:
MAGNETIC FIELDS
415
43. A circular loop of wire with a radius of 20 cm lies in the xy plane and carries a current of 2 A,
counterclockwise when viewed from a point on the positive z axis. Its magnetic dipole moment
is:
A. 0.25 A · m2 , in the positive z direction
B. 0.25 A · m2 , in the negative z direction
C. 2.5 A · m2 , in the positive z direction
D. 2.5 A · m2 , in the negative z direction
E. 0.25 A · m2 , in the xy plane
ans: A
44. The diagrams show five possible orientations of a magnetic dipole µ in a uniform magnetic field
B. For which of these does the magnetic torque on the dipole have the greatest magnitude?
. µ
....... .......
........................................
................................................ B
..
A
µ
.............................
..
........................................................................................
..
B
µ .........
..
.....
....
..
........................................................................................
..
B
B
C
........ µ
......
.....
..
..
........................................................................................
..
B
D
µ
............................
..
........................................................................................
..
B
E
ans: A
45. The magnetic dipole moment of a current-carrying loop of wire is in the positive z direction.
If a uniform magnetic field is in the positive x direction the magnetic torque on the loop is:
A. 0
B. in the positive y direction
C. in the negative y direction
D. in the positive z direction
E. in the negative z direction
ans: B
46. For a loop of current-carrying wire in a uniform magnetic field the potential energy is a minimum
if the magnetic dipole moment of the loop is:
A. in the same direction as the field
B. in the direction opposite to that of the field
C. perpendicular to the field
D. at an angle of 45◦ to the field
E. none of the above
ans: A
47. The diagrams show five possible orientations of a magnetic dipole µ in a uniform magnetic field
B. For which of these is the potential energy the greatest?
. µ
...... ........
........................................
............................................... B
..
A
µ
.............................
..
........................................................................................
..
B
B
ans: E
416
Chapter 28:
µ .........
..
.....
....
..
........................................................................................
..
MAGNETIC FIELDS
C
B
........ µ
......
.....
..
..
........................................................................................
..
D
B
µ
............................
..
........................................................................................
..
E
B
48. A loop of current-carrying wire has a magnetic dipole moment of 5 × 10−4 A · m2 . The moment
initially is aligned with a 0.5-T magnetic field. To rotate the loop so its dipole moment is
perpendicular to the field and hold it in that orientation, you must do work of:
A. 0
B. 2.5 × 10−4 J
C. −2.5 × 10−4 J
D. 1.0 × 10−3 J
E. −1.0 × 10−3 J
ans: B
Chapter 28:
MAGNETIC FIELDS
417
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
1. Suitable units for µ0 are:
A. tesla
B. newton/ampere2
C. weber/meter
D. kilogram·ampere/meter
E. tesla·meter/ampere
ans: E
2. A “coulomb” is:
A. one ampere per second
B. the quantity of charge that will exert a force of 1 N on a similar charge at a distance of 1 m
C. the amount of current in each of two long parallel wires, separated by 1 m, that produces
a force of 2 × 10−7 N/m
D. the amount of charge that flows past a point in one second when the current is 1 A
E. an abbreviation for a certain combination of kilogram, meter and second
ans: D
3. Electrons are going around a circle in a counterclockwise direction as shown. At the center of
the circle they produce a magnetic field that is:
..........
................ ...........................
.......
......
......
....
.
.
.
.
.
...
...
....
...
...
.
...
..
.
..
...
....
...
..............
.....
....
.
... ....
...
...........
..
...
...
...
..
.
.
...
.
...
...
....
...
.....
....
......
......
.
.
.
........
.
.
........................................
− electron
A.
B.
C.
D.
E.
418
into the page
out of the page
to the left
to the right
zero
ans: A
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
4. In the figure, the current element i df, the point P, and the three vectors (1, 2, 3) are all in the
plane of the page. The direction of dB, due to this current element, at the point P is:
3...
..
....
.......
..........
..
...
..
.
...
...
....
.
...
..................
...
... ..
.
.
...
.
.
...
....
....
...
...
...
....
...
.
...
.
.
...
....
...
...
...
...
....
...
.
...
.
... .......
.... .....
..
.................................................................................................................
..
i
................................................ ......
... ...
...
...
.... ....
.......................................
.
.
.
..
.
... ................................................... .....
df
2
•
P
A.
B.
C.
D.
E.
1
in the direction marked “1”
in the direction marked “2”
in the direction marked “3”
out of the page
into the page
ans: E
5. The magnitude of the magnetic field at point P, at the center of the semicircle shown, is given
by:
.. i
...................................
.
.
.
.
.
.
.....
...
...
..........
...
.. . ..............
...
...
....
..
....
.. ..
........................................ R ....•...
....................................
P
A.
B.
C.
D.
E.
2µ0 i/R
µ0 i/R
µ0 i/4πR
µ0 i/2R
µ0 i/4R
ans: E
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
419
6. The diagrams show three circuits consisting of concentric circular arcs (either half or quarter
circles of radii r, 2r, and 3r) and radial lengths. The circuits carry the same current. Rank
them according to the magnitudes of the magnetic fields they produce at C, least to greatest.
..............................
............
.......
.......
......
......
.....
.....
.....
.
.
.
....
...
.
.
...
...
...
.
.
...
.
.
.
...
....
...
...
...
...
..
..
...
..................................... ...
.................................................. ..
.
...
.
.
.
...
.
.
.
.....
........................
1
C
•
A.
B.
C.
D.
E.
..............................
............
.......
.......
......
......
.....
.....
.....
.
.
.
....
...
.
.
...
...
...
.
.
...
.
.
.
...
....
...
........................
.
.
.
.
...
...
...
...
.
.
...
..
...
..
...
....
..
..................................... .
................................................. ..
2
•
C
..............................
............
.......
.......
......
......
.....
.....
.....
.
.
.
....
.....
.
.
.
.
.
...
.
.
.
.
.
.
.
.
.
.
...
..
......
.
...
.
...
.
.
.
.
.
...
....
...
.
.
.
.
.
...
..
...
.
.
.
....
.........
.
...
.....
...
....
...
...
...
...
..
...
...
...
....................................... ....
....................
3
•
C
1, 2, 3
3, 2, 1
1, 3, 2
2, 3, 1
2, 1, 3
ans: B
7. Lines of the magnetic field produced by a long straight wire carrying a current are:
A. in the direction of the current
B. opposite to the direction of the current
C. radially outward from the wire
D. radially inward toward the wire
E. circles that are concentric with the wire
ans: E
8. In an overhead straight wire, the current is north. The magnetic field due to this current, at
our point of observation, is:
A. east
B. up
C. north
D. down
E. west
ans: E
9. A wire carrying a large current i from east to west is placed over an ordinary magnetic compass.
The end of the compass needle marked “N” will point:
A. north
B. south
C. east
D. west
E. the compass will act as an electric motor, hence the needle will keep rotating
ans: B
420
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
10. The magnetic field outside a long straight current-carrying wire depends on the distance R
from the wire axis according to:
A. R
B. 1/R
C. 1/R2
D. 1/R3
E. 1/R3/2
ans: B
11. Which graph correctly gives the magnitude of the magnetic field outside an infinitely long
straight current-carrying wire as a function of the distance r from the wire?
B
B
.
..
.
..
...
.
.
..
....
.
.
.
.
.
...........
r
A
B.
...
...
...
....
....
.....
......
..........
D
B
..
....
.
.
...
.....
.
.
.
...
.....
.
.
.
.
...
r
B
r
..........
......
.
.
.
...
...
.
.
...
..
.
.
r
C
B ..
.....
.....
.....
.....
.....
.....
.....
..
r
E
ans: D
12. The magnetic field a distance 2 cm from a long straight current-carrying wire is 2.0 × 10−5 T.
The current in the wire is:
A. 0.16 A
B. 1.0 A
C. 2.0 A
D. 4.0 A
E. 25 A
ans: C
13. Two long parallel straight wires carry equal currents in opposite directions. At a point midway
between the wires, the magnetic field they produce is:
A. zero
B. non-zero and along a line connecting the wires
C. non-zero and parallel to the wires
D. non-zero and perpendicular to the plane of the two wires
E. none of the above
ans: D
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
421
14. Two long straight wires are parallel and carry current in the same direction. The currents are
8.0 and 12 A and the wires are separated by 0.40 cm. The magnetic field in tesla at a point
midway between the wires is:
A. 0
B. 4.0 × 10−4
C. 8.0 × 10−4
D. 12 × 10−4
E. 20 × 10−4
ans: B
15. Two long straight wires are parallel and carry current in opposite directions. The currents are
8.0 and 12 A and the wires are separated by 0.40 cm. The magnetic field in tesla at a point
midway between the wires is:
A. 0
B. 4.0 × 10−4
C. 8.0 × 10−4
D. 12 × 10−4
E. 20 × 10−4
ans: E
16. Two long straight current-carrying parallel wires cross the x axis and carry currents I and 3I
in the same direction, as shown. At what value of x is the net magnetic field zero?
x
0
1
3
.
......
........
....
A.
B.
C.
D.
E.
422
I
4
5
7
.
......
........
....
3I
0
1
3
5
7
ans: C
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
17. Two long straight wires pierce the plane of the paper at vertices of an equilateral triangle as
shown below. They each carry 2 A, out of the paper. The magnetic field at the third vertex
(P) has magnitude (in T):
P
....
... ...
... ....
...
...
.
...
...
...
..
...
...
.
...
.
...
...
.
...
..
.
...
.
.
...
.
..
...
.
.
...
...
.
...
.
.
.
...
...
...
.
.
...
.
.
.•
..
.•
.
•
•
•
•
.•
•
•
•
•
•
•
.
•
•
•
•
.•
•
•
•
•
•
•
•
•
•
•
•
•
•
..•
.•
•
•
•
•
•
•
•
•
•
•
.•
.•
..•
......................................................................................•
•
•
•
•
•
•
•
•
•
•
•
•
•
4 cm
2 A •••••••••••••••••••••••
A.
B.
C.
D.
E.
4 cm
4 cm
• 2A
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
1.0 × 10−5
1.7 × 10−5
2.0 × 10−5
5.0 × 10−6
8.7 × 10−6
ans: B
18. The diagram shows three equally spaced wires that are perpendicular to the page. The currents
are all equal, two being out of the page and one being into the page. Rank the wires according
to the magnitudes of the magnetic forces on them, from least to greatest.
.................
...
..
....
.
.... ......
.........
.................
...
..
....
.
.... ......
.........
.................
...
..
....
.
.... ......
.........
1
2
3
·
A.
B.
C.
D.
E.
×
·
1, 2, 3
2, 1 and 3 tie
2 and 3 tie, then 1
1 and 3 tie, then 2
3, 2, 1
ans: B
19. Two parallel wires carrying equal currents of 10 A attract each other with a force of 1 mN. If
both currents are doubled, the force of attraction will be:
A. 1 mN
B. 4 mN
C. 0.5 mN
D. 0.25 mN
E. 2 mN
ans: B
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
423
20. Two parallel long wires carry the same current and repel each other with a force F per unit
length. If both these currents are doubled and the wire separation tripled, the force per unit
length becomes:
A. 2F/9
B. 4F/9
C. 2F/3
D. 4F/3
E. 6F
ans: D
21. Two parallel wires, 4 cm apart, carry currents of 2 A and 4 A respectively, in the same direction.
The force per unit length in N/m of one wire on the other is:
A. 1 × 10−3 , repulsive
B. 1 × 10−3 , attractive
C. 4 × 10−5 , repulsive
D. 4 × 10−5 , attractive
E. none of these
ans: D
22. Two parallel wires, 4 cm apart, carry currents of 2 A and 4 A respectively, in opposite directions.
The force per unit length in N/m of one wire on the other is:
A. 1 × 10−3 , repulsive
B. 1 × 10−3 , attractive
C. 4 × 10−5 , repulsive
D. 4 × 10−5 , attractive
E. none of these
ans: C
23. Four long straight wires carry equal currents into the page as shown. The magnetic force
exerted on wire F is:
F
A.
B.
C.
D.
E.
424
north
east
south
west
zero
ans: B
Chapter 29:
N
W
E
S
MAGNETIC FIELDS DUE TO CURRENTS
24. A constant current is sent through a helical coil. The coil:
A. tends to get shorter
B. tends to get longer
C. tends to rotate about its axis
D. produces zero magnetic field at its center
E. none of the above
ans: A
25. The diagram shows three arrangements of circular loops, centered on vertical axes and carrying identical currents in the directions indicated. Rank the arrangements according to the
magnitudes of the magnetic fields at the midpoints between the loops on the central axes.
............................................
.......
....
...
...
.....
..
....
...
.
.......
.
.
.
............................................
.....
•
A.
B.
C.
D.
E.
............................................
.......
....
...
...
.....
..
....
...
.
.......
.
.
.
............................................
.....
•
..........
................... ..........................
........
............................. .......
...... .............
...... ....
.... ..
.... ......
..
.
..... .....
...
..
... ....
.. ....
.
.
.... .......
.
.
.
...
. ...
......
.
......... ............................................. .............
.................................................
......
•
...........................................
.......
....
...
....
.
.....
...
....
....
.......
.
.
.
.
.
.........................................
......
...........................................
.......
....
...
....
.
.....
...
....
....
....... .
.
.
.
.
.
.........................................
.
.
...
...........................................
.......
....
...
....
.
.....
...
....
....
.......
.
.
.
.
.
.........................................
......
1
2
3
1, 2, 3
2, 1, 3
2, 3, 1
3, 2, 1
3, 1, 2
ans: C
26. Helmholtz coils are commonly used in the laboratory because the magnetic field between them:
A. can be varied more easily than the fields of other current arrangements
B. is especially strong
C. nearly cancels Earth’s magnetic field
D. is parallel to the plane of the coils
E. is nearly uniform
ans: E
27. If the radius of a pair of Helmholtz coils is R then the distance between the coils is:
A. R/4
B. R/2
C. R
D. 2R
E. 4R
ans: C
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
425
28. If R is the distance from a magnetic dipole, then the magnetic field it produces is proportional
to:
A. R
B. 1/R
C. R2
D. 1/R2
E. 1/R3
ans: E
29. A square loop of current-carrying wire with edge length a is in the xy plane, the origin being
at its center. Along which of the following lines can a charge move without experiencing a
magnetic force?
A. x = 0, y = a/2
B. x = a/2, y = a/2
C. x = a/2, y = 0
D. x = 0, y = 0
E. x = 0, z = 0
ans: D
30. In Ampere’s law, B · ds = µ0 i, the integration must be over any:
A. surface
B. closed surface
C. path
D. closed path
E. closed path that surrounds all the current producing B
ans: D
31. In Ampere’s law, B · ds = µ0 i, the symbol ds is:
A. an infinitesimal piece of the wire that carries current i
B. in the direction of B
C. perpendicular to B
D. a vector whose magnitude is the length of the wire that carries current i
E. none of the above
ans: E
32. In Ampere’s law, B · ds = µ0 i, the direction of the integration around the path:
A. must be clockwise
B. must be counterclockwise
C. must be such as to follow the magnetic field lines
D. must be along the wire in the direction of the current
E. none of the above
ans: E
426
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
33. A long straight wire carrying a 3.0 A current enters a room through a window 1.5 m high and
1.0 m wide. The path integral B · ds around the window frame has the value (in T·m):
A. 0.20
B. 2.5 × 10−7
C. 3.0 × 10−7
D. 3.8 × 10−6
E. none of these
ans: D
34. Two long straight wires enter a room through a door. One carries a current of 3.0 A into
the
room while the other carries a current of 5.0 A out. The magnitude of the path integral B · ds
around the door frame is:
A. 2.5 × 10−6 T · m
B. 3.8 × 10−6 T · m
C. 6.3 × 10−6 T · m
D. 1.0 × 10−5 T · m
E. none of these
ans: A
35. If the magnetic field B is uniform over the area bounded by a circle with radius R, the net
current through the circle is:
A. 0
B. 2πRB/µ0
C. πR2 B/µ0
D. RB/2µ0
E. 2RB/µ0
ans: A
36. The magnetic field at any point is given by B = Ar × k̂, where r is the position vector of the
point and A is a constant. The net current through a circle of radius R, in the xy plane and
centered at the origin is given by:
A. πAR2 /µ0
B. 2πAR/µ0
C. 4πAR3 /3µ0
D. 2πAR2 /µ0
E. πAR2 /2µ0
ans: D
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
427
37. A hollow cylindrical conductor (inner radius = a, outer radius = b) carries a current i uniformly
spread over its cross section. Which graph below correctly gives B as a function of the distance
r from the center of the cylinder?
B
B ...............................
...
...
...
...
...
...
...
..................................
..
...
..
...
...
..
...
..
...
..
....
..
........
r
a
b
B
r
a
b
.........
.... .....
.
.
.
...
..
...
...
...
....
..
......
..
..... r
a
b
B
A
B
.....
... ....
.
.
... .....
...
...
.
.
.
...
...
....
.
.
.
........
...
r
a
b
D
C
B
.....................................
...
...
.
.
.
...
...
.
...
.
.
.
...
..
.
....
.
..
.......
.
.
... r
..
a
b
E
ans: C
38. A long straight cylindrical shell carries current i parallel to its axis and uniformly distributed
over its cross section. The magnitude of the magnetic field is greatest:
A. at the inner surface of the shell
B. at the outer surface of the shell
C. inside the shell near the middle
D. in hollow region near the inner surface of the shell
E. near the center of the hollow region
ans: B
39. A long straight cylindrical shell has inner radius Ri and outer radius Ro . It carries current
i, uniformly distributed over its cross section. A wire is parallel to the cylinder axis, in the
hollow region (r < Ri ). The magnetic field is zero everywhere outside the shell (r > Ro ). We
conclude that the wire:
A. is on the cylinder axis and carries current i in the same direction as the current in the shell
B. may be anywhere in the hollow region but must be carrying current i in the direction
opposite to that of the current in the shell
C. may be anywhere in the hollow region but must be carrying current i in the same direction
as the current in the shell
D. is on the cylinder axis and carries current i in the direction opposite to that of the current
in the shell
E. does not carry any current
ans: D
428
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
40. A long straight cylindrical shell has inner radius Ri and outer radius Ro . It carries a current i,
uniformly distributed over its cross section. A wire is parallel to the cylinder axis, in the hollow
region (r < Ri ). The magnetic field is zero everywhere in the hollow region. We conclude that
the wire:
A. is on the cylinder axis and carries current i in the same direction as the current in the shell
B. may be anywhere in the hollow region but must be carrying current i in the direction
opposite to that of the current in the shell
C. may be anywhere in the hollow region but must be carrying current i in the same direction
as the current in the shell
D. is on the cylinder axis and carries current i in the direction opposite to that of the current
in the shell
E. does not carry any current
ans: E
41. The magnetic field B inside a long ideal solenoid is independent of:
A. the current
B. the core material
C. the spacing of the windings
D. the cross-sectional area of the solenoid
E. the direction of the current
ans: D
42. Two long ideal solenoids (with radii 20 mm and 30 mm, respectively) have the same number
of turns of wire per unit length. The smaller solenoid is mounted inside the larger, along a
common axis. The magnetic field within the inner solenoid is zero. The current in the inner
solenoid must be:
A. two-thirds the current in the outer solenoid
B. one-third the current in the outer solenoid
C. twice the current in the outer solenoid
D. half the current in the outer solenoid
E. the same as the current in the outer solenoid
ans: E
43. Magnetic field lines inside the solenoid shown are:
.........................................
.............
.......
.......
....
....
...
.....
.
....
...........
..... ....
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
...............................................
............................................................................................................................
.......
..
.
......
.......
..... .......
...... ...
..... ...
... .......
....................
.
....... .
....... ..................... .................................. ...............
......
.........................
..
.
.
.
...
..
... .. .
.... ......................................................................... ..........
..
...
...
............
........
........ ....
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.................................................................................... ................................... .................................
..
....
...
..
..
.....
..
.....
...
.
.
........
.
.
.
.
..................... .......................
..........
I
I
A.
B.
C.
D.
E.
clockwise circles as one looks down the axis from the top of the page
counterclockwise circles as one looks down the axis from the top of the page
toward the top of the page
toward the bottom of the page
in no direction since B = 0
ans: C
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
429
44. Solenoid 2 has twice the radius and six times the number of turns per unit length as solenoid
1. The ratio of the magnetic field in the interior of 2 to that in the interior of 1 is:
A. 2
B. 4
C. 6
D. 1
E. 1/3
ans: C
45. A solenoid is 3.0 cm long and has a radius of 0.50 cm. It is wrapped with 500 turns of wire
carrying a current of 2.0 A. The magnetic field at the center of the solenoid is:
A. 9.9 × 10−8 T
B. 1.3 × 10−3 T
C. 4.2 × 10−2 T
D. 16 T
E. 20 T
ans: C
46. A toroid with a square cross section carries current i. The magnetic field has its largest
magnitude:
A. at the center of the hole
B. just inside the toroid at its inner surface
C. just inside the toroid at its outer surface
D. at any point inside (the field is uniform)
E. none of the above
ans: B
47. A toroid has a square cross section with the length of an edge equal to the radius of the inner
surface. The ratio of the magnitude of the magnetic field at the inner surface to the magnitude
of the field at the outer surface is:
A. 1/4
B. 1/2
C. 1
D. 2
E. 4
ans: D
430
Chapter 29:
MAGNETIC FIELDS DUE TO CURRENTS
Chapter 30:
INDUCTION AND INDUCTANCE
1. The normal to a certain 1-m2 area makes an angle of 60◦ with a uniform magnetic field.
The magnetic flux through this area is the same as the flux through a second area that is
perpendicular to the field if the second area is:
A. 0.866 m2
B. 1.15 m2
C. 0.5 m2
D. 2 m2
E. 1 m2
ans: C
2. Suppose this page is perpendicular to a uniform magnetic field and the magnetic flux through
it is 5 Wb. If the page is turned by 30◦ around an edge the flux through it will be:
A. 2.5 Wb
B. 4.3 Wb
C. 5 Wb
D. 5.8 Wb
E. 10 Wb
ans: B
3. A 2-T uniform magnetic field makes an angle of 30◦ with the z axis. The magnetic flux through
a 3-m2 portion of the xy plane is:
A. 2.0 Wb
B. 3.0 Wb
C. 5.2 Wb
D. 6.0 Wb
E. 12 Wb
ans: C
4. A uniform magnetic field makes an angle of 30◦ with the z axis. If the magnetic flux through
a 1-m2 portion of the xy plane is 5 Wb then the magnetic flux through a 2-m2 portion of the
same plane is:
A. 2.5 Wb
B. 4.3 Wb
C. 5 Wb
D. 5.8 Wb
E. 10 Wb
ans: E
5. 1 weber is the same as:
A. 1 V/s
B. 1 T/s
C. 1 T/m
D. 1 T · m2
2
E. 1 T/m
ans: D
Chapter 30:
INDUCTION AND INDUCTANCE
431
6. 1 weber is the same as:
A. 1 V · s
B. 1 T · s
C. 1 T/m
D. 1 V/s
E. 1 T/m2
ans: A
7. The units of motional emf are:
A. volt/second
B. volt·meter/second
C. volt/tesla
D. tesla/second
E. tesla·meter2 /second
ans: E
8. Faraday’s law states that an induced emf is proportional to:
A. the rate of change of the magnetic field
B. the rate of change of the electric field
C. the rate of change of the magnetic flux
D. the rate of change of the electric flux
E. zero
ans: C
9. The emf that appears in Faraday’s law is:
A. around a conducting circuit
B. around the boundary of the surface used to compute the magnetic flux
C. throughout the surface used to compute the magnetic flux
D. perpendicular to the surface used to compute the magnetic flux
E. none of the above
ans: B
10. If the magnetic flux through a certain region is changing with time:
A. energy must be dissipated as heat
B. an electric field must exist at the boundary
C. a current must flow around the boundary
D. an emf must exist around the boundary
E. a magnetic field must exist at the boundary
ans: D
432
Chapter 30:
INDUCTION AND INDUCTANCE
11. A square loop of wire lies in the plane of the page. A decreasing magnetic field is directed into
the page. The induced current in the loop is:
A. counterclockwise
B. clockwise
C. zero
D. up the left edge and from right to left along the top edge
E. through the middle of the page
ans: B
12. As an externally generated magnetic field through a certain conducting loop increases in magnitude, the field produced at points inside the loop by the current induced in the loop must
be:
A. increasing in magnitude
B. decreasing in magnitude
C. in the same direction as the applied field
D. directed opposite to the applied field
E. perpendicular to the applied field
ans: D
13. At any instant of time the total magnetic flux through a stationary conducting loop is less in
magnitude than the flux associated with an externally applied field. This might occur because:
A. the applied field is normal to the loop and increasing in magnitude
B. the applied field is normal to the loop and decreasing in magnitude
C. the applied field is parallel to the plane of the loop and increasing in magnitude
D. the applied field is parallel to the plane of the loop and decreasing in magnitude
E. the applied field is tangent to the loop
ans: A
14. A long straight wire is in the plane of a rectangular conducting loop. The straight wire carries
a constant current i, as shown. While the wire is being moved toward the rectangle the current
in the rectangle is:
i
A.
B.
C.
D.
E.
..
......
... ...
zero
clockwise
counterclockwise
clockwise in the left side and counterclockwise in the right side
counterclockwise in the left side and clockwise in the right side
ans: C
Chapter 30:
INDUCTION AND INDUCTANCE
433
15. A long straight wire is in the plane of a rectangular conducting loop. The straight wire carries
an increasing current in the direction shown. The current in the rectangle is:
i
A.
B.
C.
D.
E.
.....
.. ..
.. ..
zero
clockwise
counterclockwise
clockwise in the left side and counterclockwise in the right side
counterclockwise in the left side and clockwise in the right side
ans: C
16. A long straight wire is in the plane of a rectangular conducting loop. The straight wire initially
carries a constant current i in the direction shown. While the current i is being shut off, the
current in the rectangle is:
i
A.
B.
C.
D.
E.
434
....
.....
.. ..
zero
clockwise
counterclockwise
clockwise in the left side and counterclockwise in the right side
counterclockwise in the left side and clockwise in the right side
ans: B
Chapter 30:
INDUCTION AND INDUCTANCE
17. A rectangular loop of wire is placed midway between two long straight parallel conductors as
shown. The conductors carry currents i 1 and i2 , as indicated. If i1 is increasing and i2 is
constant, then the induced current in the loop is:
.....
i1 ........
A.
B.
C.
D.
E.
...
.....
... ..
i2
zero
clockwise
counterclockwise
depends on i1 − i2
depends on i1 + i2
ans: C
18. You push a permanent magnet with its north pole away from you toward a loop of conducting
wire in front of you. Before the north pole enters the loop the current in the loop is:
A. zero
B. clockwise
C. counterclockwise
D. to your left
E. to your right
ans: C
19. A vertical bar magnet is dropped through the center of a horizontal loop of wire, with its north
pole leading. At the instant when the midpoint of the magnet is in the plane of the loop, the
induced current at point P, viewed from above, is:
A. maximum and clockwise
B. maximum and counterclockwise
C. not maximum but clockwise
D. not maximum but counterclockwise
E. essentially zero
ans: E
20. A circular loop of wire rotates about a diameter in a magnetic field that is perpendicular to
the axis of rotation. Looking in the direction of the field at the loop the induced current is:
A. always clockwise
B. always counterclockwise
C. clockwise in the lower half of the loop and counterclockwise in the upper half
D. clockwise in the upper half of the loop and counterclockwise in the lower half
E. sometimes clockwise and sometimes counterclockwise
ans: E
Chapter 30:
INDUCTION AND INDUCTANCE
435
21. In the experiment shown:
....
S..............
.......................................
.. ........ ........ ........ .....
...
.............................•
.•
............................................. •
... .. ... .. ... .. •
.
....
...... ...... ...... ...
.
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
....
.
.
............................................................................................................................................................................................
..
...
..
..
A.
B.
C.
D.
E.
......... ......... ......... .........
•......... ...................... ...................... ...................... •.................................................. ......
..
...
...
...
..
...
.........
.
.
.
.
.
.
...
.
.
...
...
.
...
...
.
..
..
...
.
...
..
...
...
..
.
...
.
.
...... ......
..........
...
...
...
...
...
...
...
...
..
.........................................................................................................................
G
there is a steady reading in G as long as S is closed
a motional emf is generated when S is closed
the current in the battery goes through G
there is a current in G just after S is opened or closed
since the two loops are not connected, the current in G is always zero
ans: D
22. The emf developed in a coil X due to the current in a neighboring coil Y is proportional to the:
A. magnetic field in X
B. rate of change of magnetic field in X
C. resistance of X
D. thickness of the wire in X
E. current in Y
ans: B
23. One hundred turns of insulated copper wire are wrapped around an iron core of cross-sectional
area 0.100 m2 . The circuit is completed by connecting the coil to a 10-Ω resistor. As the
magnetic field along the coil axis changes from 1.00 T in one direction to 1.00 T in the other
direction, the total charge that flows through the resistor is:
A. 10−2 C
B. 2 × 10−2 C
C. 1 C
D. 2 C
E. 0.20 C
ans: D
436
Chapter 30:
INDUCTION AND INDUCTANCE
24. In the circuit shown, there will be a non-zero reading in galvanometer G:
.............................................................................................................................
..
..
....
...
...
.
....
.........
...
..
...
.
...
.........................
........ ..
....
.
.
.
.
.
.
.
.
.
.
.
.
.
.....................
...
..
..
................................
....
..
..
...
...
........
.
....
..
....
.
.
.
.
.
....
..
...
....
....
.
...
...................................... ...
............................ ..
•
•
A.
B.
C.
D.
E.
S
•
•
.....................................................................................................
..
..
....
...
...
.
...
....
.
.
.
.
...
.
.
...
....
.
..........
.................
.
.
.
.
.
.
....
....
.
...................
.
...
..
.................
.
..
...
..................
...
...
... .............
...
.....
.
....................
..................
...
...
.....
...
.....
...
....
...
..
...
..
.......................................................................... ....
•
G
•
only just after S is closed
only just after S is opened
only while S is kept closed
never
only just after S is opened or closed
ans: E
25. A magnet moves inside a coil. Consider the following factors:
I. strength of the magnet
II. number of turns in the coil
III. speed at which the magnet moves
Which can affect the emf induced in the coil?
A. I only
B. II only
C. III only
D. I and II only
E. I, II, III
ans: E
26. The graph shows the magnitude B of a uniform magnetic field that is perpendicular to the
plane of a conducting loop. Rank the five regions indicated on the graph according to the
magnitude of the emf induced in the loop, from least to greatest.
B
2
.........................................................
.
.
.....
...
..... 3
...
.
.....
.
..
.....
.
.
1....
.....
.
.....
.
..
.....
.
.
.
.
.......
..
........ 4
.
.
.
.
........
..
........
.
.
........
.
....
...
t
A.
B.
C.
D.
E.
1, 2, 3,
2, 4, 3,
4, 3, 1,
1, 3, 4,
4, 3, 2,
ans: B
4
1
2
2
1
Chapter 30:
INDUCTION AND INDUCTANCE
437
27. The circuit shown is in a uniform magnetic field that is into the page. The current in the circuit
is 0.20 A. At what rate is the magnitude of the magnetic field changing? Is it increasing or
decreasing?:
←−− 12 cm −−→
↑
|
|
12 cm
|
|
↓
.. .. ..
...................................................................................................... ..
...
...
.. .. ..
...
...
...
...
....
....
...
...
...
...
...
...
...
...
...
...
.....
.....
...
...
...
...
....
....
...
...
...
...
...
...
...
...
.
...
.......................................... ........................................................
10 Ω
4V
A.
B.
C.
D.
E.
zero
140 T/s,
140 T/s,
420 T/s,
420 T/s,
ans: B
decreasing
increasing
decreasing
increasing
28. A changing magnetic field pierces the interior of a circuit containing three identical resistors.
Two voltmeters are connected to the same points, as shown. V1 reads 1 mV. V2 reads:
......................
....
...
..
.......................................... ....
..........................................................
...
....
....
.... 2 .....
..................
...
...
....
...
..
..
...
...
....
....
..
..
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
....................................................................... ....... ....... ................................. ...... ....... .............................................................. ..
.. .. ..
...
.. .. ..
...
..
.
....
...
...
.
.
...
...
.
...
...
.....
....
...
...
.
.
...
...
....
...
....
...
...
....
....
...
...
..
..
...
..
...
.
.
.
.
.
.
.
.
.
.
.
.
...
........................................................ ....... ....... ............................................... .
....
.. .. ..
...
...
...
...
...
...
...
...
...
...
...
...
...
.
.
.
.
.
.
.
.
.
.
.
.
.....
...
...
.....
.
.
.
.
...
..
................................................................................. ....
.
..........................................................................................................
...
.
...
1
.
.
.....
..................
V
R
•
R
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
R
V
A.
B.
C.
D.
E.
438
0
1/3 mV
1/2 mV
1 mV
2 mV
ans: E
Chapter 30:
INDUCTION AND INDUCTANCE
•
29. A circular loop of wire is positioned half in and half out of a square region of constant uniform
magnetic field directed into the page, as shown. To induce a clockwise current in this loop:
⊗
⊗
⊗
⊗
⊗
A.
B.
C.
D.
E.
⊗
⊗
⊗
⊗
⊗
⊗
⊗
y
⊗
⊗
⊗•••••••••••••••••••••••••••••••••••••••••
•
•
•
B ⊗ ⊗ ⊗ ⊗ ••••••••⊗ •••••••• loop
•
•
⊗ ⊗ ⊗ ⊗ ••••••••••••••••••••••••••••
⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗
⊗
⊗
⊗
x
move it in +x direction
move it in +y direction
move it in −y direction
move it in −x direction
increase the strength of the magnetic field
ans: A
30. The four wire loops shown have edge lengths of either L, 2L, or 3L. They will move with the
same speed into a region of uniform magnetic field B, directed out of the page. Rank them
according to the maximum magnitude of the induced emf, least to greatest.
.....
.......................................................................
....
1
A.
B.
C.
D.
E.
2
3
4
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1 and 2 tie, then 3 and 4 tie
3 and 4 tie, then 1 and 2 tie
4, 2, 3, 1
1, then 2 and 3 tie, then 4
1, 2, 3, 4
ans: D
Chapter 30:
INDUCTION AND INDUCTANCE
439
31. A square loop of wire moves with a constant speed v from a field-free region into a region
of constant uniform magnetic field, as shown. Which of the five graphs correctly shows the
induced current i in the loop as a function of time t?
⊗
⊗
v
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
.
•
•
•
• ................................................
....
•
•
•
•
•
..
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
⊗
⊗
⊗
i
.
.........
.
.
.
... ...
... ..
A
.....
.. .....
.. .....
.. ....
i
i
t
...
... ....
.
.
. .
... ..
... ..
......................
...
..
..
..
...
..
⊗
⊗
⊗
⊗
B
D
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
t
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗ B
⊗
⊗
i
......................
...
..
..
..
...
..
i
... ....
... ...
... ....
......
⊗
t
......................
...
..
..
..
...
..
E
..............................
.
.
....
...
....
...
.
....
.
.
...
C
...
...
...
..
...
.
..
....................
t
t
ans: C
32. The figure shows a bar moving to the right on two conducting rails. To make an induced
current i in the direction indicated, a constant magnetic field in region A should be in what
direction?
i
.
..........................................................
..
i
...
...
...
...
...
.
..........
........
..
A
i
.......
..........
...
...
...
..
...
v
..
..................................................
..
..
..................................................
..
i
A.
B.
C.
D.
E.
440
Right
Left
Into the page
Out of the page
Impossible; this cannot be done with a constant magnetic field
ans: C
Chapter 30:
INDUCTION AND INDUCTANCE
33. A car travels northward at 75 km/h along a straight road in a region where Earth’s magnetic
field has a vertical component of 0.50 × 10−4 T. The emf induced between the left and right
side, separated by 1.7 m, is:
A. 0
B. 1.8 mV
C. 3.6 mV
D. 6.4 mV
E. 13 mV
ans: B
34. Coils P and Q each have a large number of turns of insulated wire. When switch S is closed,
the pointer of galvanometer G is deflected toward the left. With S now closed, to make the
pointer of G deflect toward the right one could:
..........................
... ... .... ....
... ... .... ....
.... ....
.. ..
.. ..
. .
... ...
.. ..
.. ..
... ...
.... ....
.. ..
... ...
... ...
... ...
... ...
.. ...
.
... ...
.. ...
.
... ...
.. ..
... ... .... ....
... ... ... ...
.... ...... ...
.................
.... ....
... ...
.. ...
......................................................................................................................................... ....
...
...
...
..
...
...
...
.........
...
.........
..
.
.
.
.
.
.
.
.
.....
.
...
...... ....... .......
.
.
.
.
... ... ... ... ... ... ............................................... .. ......................................
..... ..... .....
P
• •
S
R
A.
B.
C.
D.
E.
..........................
... ... .... ....
... ... .... ....
.... ....
.. ..
.. ..
. .
... ...
.. ..
.. ..
... ...
.... ....
.. ..
... ...
... ...
... ...
... ...
.. ...
.
... ...
.. ...
.
... ...
.. ..
... ... .... ....
... ... ... ...
.... ...... ...
................
.... ....
... ...
... ...
......................................................................................................................................................................
...
..
...
...
...
...
...
...
...
...
....................
.
...
...
...
.
........................................................ ....
........................................................ ..
...
.
....
.
.
.
..............
Q
G
move the slide of the rheostat R quickly to the right
move coil P toward coil Q
move coil Q toward coil P
open S
do none of the above
ans: D
35. A rod lies across frictionless rails in a constant uniform magnetic field B, as shown. The
rod moves to the right with speed v. In order for the emf around the circuit to be zero, the
magnitude of the magnetic field should:
...... ........................... v
.......................................................... ........................
.. ................................................. .....................
..
.. ... ⊗
⊗ .. ... ⊗
.. ..
.. ...
.. ..
⊗
.. ... ⊗
.. ..
⊗ ... .... ⊗
.. .. ⊗
. .............................................. ....................
.......................................................... ........................
......
A.
B.
C.
D.
E.
not change
increase linearly with time
decrease linearly with time
increase quadratically with time
decrease quadratically with time
ans: C
Chapter 30:
INDUCTION AND INDUCTANCE
441
36. A rectangular loop of wire has area A. It is placed perpendicular to a uniform magnetic field
B and then spun around one of its sides at frequency f . The maximum induced emf is:
A. BAf
B. BAf
C. 2BAf
D. 2πBAf
E. 4πBAf
ans: D
37. A rectangular loop of wire is placed perpendicular to a uniform magnetic field and then spun
around one of its sides at frequency f . The induced emf is a maximum when:
A. the flux is zero
B. the flux is a maximum
C. the flux is half its maximum value
D. the derivative of the flux with respect to time is zero
E. none of the above
ans: A
38. The diagram shows a circular loop of wire that rotates at a steady rate about a diameter O
that is perpendicular to a uniform magnetic field. The maximum induced emf occurs when the
point X on the loop passes:
e
•
.....................................................................................................................................................................................
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
••
•
•
•
•
•
•
............................................................................................•
..............•
...........................................................................
•
•
• •
•
•
•
•
• •
•
•
•
•
•
• •
•
•
•
•
• •
•
•
•
•
•
•
•
•
............................................................................................•
..............•
...........................................................................
•
•
•
•
•
•
• •
•
•
•
• •
•
•
•
•
•
• •
•
•
•
•
• •
•
•
•
............................................................................................•
..............•
...........................................................................
•
•
•
•
•
••
•
•
•
•
•
•
•
•
•
••
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
d•
c•
•
b
•O
•
a
X
.....................................................................................................................................................................................
A.
B.
C.
D.
E.
........
...
........
........
...
........
........
...
........
B
........
...
........
........
...
........
a
b
c
d
e
ans: C
39. A copper hoop is held in a vertical east-west plane in a uniform magnetic field whose field lines
run along the north-south direction. The largest induced emf is produced when the hoop is:
A. rotated about a north-south axis
B. rotated about an east-west axis
C. moved rapidly, without rotation, toward the east
D. moved rapidly, without rotation, toward the south
E. moved rapidly, without rotation, toward the northwest
ans: B
442
Chapter 30:
INDUCTION AND INDUCTANCE
40. A 10-turn conducting loop with a radius of 3.0 cm spins at 60 revolutions per second in a
magnetic field of 0.50 T. The maximum emf generated is:
A. 0.014 V
B. 0.53 V
C. 5.3 V
D. 18 V
E. 180 V
ans: C
41. A single loop of wire with a radius of 7.5 cm rotates about a diameter in a uniform magnetic
field of 1.6 T. To produce a maximum emf of 1.0 V, it should rotate at:
A. 0
B. 2.7 rad/s
C. 5.6 rad/s
D. 35 rad/s
E. 71 rad/s
ans: D
42. A merry-go-round has an area of 300 m2 and spins at 2 rpm about a vertical axis at a place
where Earth’s magnetic field is vertical and has a magnitude of 5 × 10−5 T. The emf around
the rim is:
A. 0
B. 0.5 mV
C. 3.1 mV
D. 15 mV
E. 30 mV
ans: A
Chapter 30:
INDUCTION AND INDUCTANCE
443
43. A copper penny slides on a horizontal frictionless table. There is a square region of constant
uniform magnetic field perpendicular to the table, as shown. Which graph correctly shows the
speed v of the penny as a function of time t?
top view
⊗
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
..
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
....
•
•
•
•
•
•
•
•
•
•
•
• .........................................
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
. .
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
v
•
⊗
⊗
⊗
v
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
⊗
B
⊗
v
.........................................................................
v
................
.............
...
....
..................................
t
...............
...............
.............
.............
.
..............
t
A
t
B
v
C
v
......................
.....................
...
....................
..................
......
.......
.......
............................
t
D
t
E
ans: D
44. A rod with resistance R lies across frictionless conducting rails in a constant uniform magnetic
field B, as shown. Assume the rails have negligible resistance. The magnitude of the force that
must be applied by a person to pull the rod to the right at constant speed v is:
↑
|
L
|
↓
A.
B.
C.
D.
E.
444
←−−− x −−−→
........ ..................................
.
............................................................................ ...........................v...
. ..
..
.
.. ................................................................... ...........................
.. ..
.. ...
.. ..
.. ...
.. ...
.. ..
.. ...
.. ..
.. ..
.. ...
. ..
.. ..
.. .................................................................. ..............................
............................................................................. .............................
........
0
BLv
BLv/R
B 2 L2 v/R
B 2 Lxv/R
ans: D
Chapter 30:
INDUCTION AND INDUCTANCE
45. A rod of length L and electrical resistance R moves through a constant uniform magnetic field
B, perpendicular to the rod. The force that must be applied by a person to keep the rod
moving with constant velocity v is:
A. 0
B. BLv
C. BLv/R
D. B 2 L2 v/R
E. B 2 L2 v 2 /R
ans: A
46. As a loop of wire with a resistance of 10 Ω moves in a constant non-uniform magnetic field, it
loses kinetic energy at a uniform rate of 4.0 mJ/s. The induced current in the loop:
A. is 0
B. is 2 mA
C. is 2.8 mA
D. is 20 mA
E. cannot be calculated from the given data
ans: D
47. As a loop of wire with a resistance of 10 Ω moves in a non-uniform magnetic field, it loses
kinetic energy at a uniform rate of 5 mJ/s. The induced emf in the loop:
A. is 0
B. is 0.2 V
C. is 0.28 V
D. is 2 V
E. cannot be calculated from the given data
ans: B
48. An
A.
B.
C.
D.
E.
electric field is associated with every:
magnetic field
time-dependent magnetic field
time-dependent magnetic flux
object moving in a magnetic field
conductor moving in a magnetic field
ans: B
49. A cylindrical region of radius R = 3.0 cm contains a uniform magnetic field parallel to its
axis. If the electric field induced at a point R/2 from the cylinder axis is 4.5 × 10−3 V/m the
magnitude of the magnetic field must be changing at the rate:
A. 0
B. 0.30 T/s
C. 0.60 T/s
D. 1.2 T/s
E. 2.4 T/s
ans: C
Chapter 30:
INDUCTION AND INDUCTANCE
445
50. A cylindrical region of radius R contains a uniform magnetic field parallel to its axis. The field
is zero outside the cylinder. If the magnitude of the field is changing at the rate dB/dt, the
electric field induced at a point 2R from the cylinder axis is:
A. zero
B. 2R dB/dt
C. R dB/dt
D. (R/2) dB/dt
E. (R/4) dB/dt
ans: E
51. A cylindrical region of radius R contains a uniform magnetic field, parallel to its axis, with
magnitude that is changing linearly with time. If r is the radial distance from the cylinder
axis, the magnitude of the induced electric field inside the cylinder is proportional to:
A. R
B. r
C. r 2
D. 1/r
E. 1/r2
ans: B
52. A cylindrical region of radius R contains a uniform magnetic field, parallel to its axis, with
magnitude that is changing linearly with time. If r is the radial distance from the cylinder
axis, the magnitude of the induced electric field outside the cylinder is proportional to:
A. R
B. r
C. r 2
D. 1/r
E. 1/r2
ans: D
53. The unit “henry” is equivalent to:
A. volt·second/ampere
B. volt/second
C. ohm
D. ampere·volt/second
E. ampere·second/volt
ans: A
446
Chapter 30:
INDUCTION AND INDUCTANCE
54. The diagram shows an inductor that is part of a circuit. The direction of the emf induced in
the inductor is indicated. Which of the following is possible?
E ◦−→
.......
.......
.......
.......
.. ...
.. ...
.. ...
.. ...
.. ... .. ... .. ... .. ...
....................................................... ..
.... . ... .... ... .... ... .... ...
........................................................
...
... .. ... .. ... .. ... ...
...
... ...
... ...
... ...
...
... ...
...
.
.
.
......
.....................................................................................................................
A.
B.
C.
D.
E.
The current is constant and rightward
The current is constant and leftward
The current is increasing and rightward
The current is increasing and leftward
None of the above
ans: D
55. A 10-turn ideal solenoid has an inductance of 3.5 mH. When the solenoid carries a current of
2.0 A the magnetic flux through each turn is:
A. 0
B. 3.5 × 10−4 wb
C. 7.0 × 10−4 wb
D. 7.0 × 10−3 wb
E. 7.0 × 10−2 wb
ans : C
56. A 10-turn ideal solenoid has an inductance of 4.0 mH. To generate an emf of 2.0 V the current
should change at a rate of:
A. zero
B. 5.0 A/s
C. 50 A/s
D. 250 A/s
E. 500 A/s
ans: E
57. A long narrow solenoid has length
area A. Its inductance is:
A. µ0 N 2 A
B. µ0 N 2 A/
C. µ0 N A/
D. µ0 N 2 /A
E. none of these
ans: B
and a total of N turns, each of which has cross-sectional
Chapter 30:
INDUCTION AND INDUCTANCE
447
58. A flat coil of wire, having 5 turns, has an inductance L. The inductance of a similar coil having
20 turns is:
A. 4L
B. L/4
C. 16L
D. L/16
E. L
ans: C
59. An inductance L, resistance R, and ideal battery of emf E are wired in series. A switch in the
circuit is closed at time 0, at which time the current is zero. At any later time t the current i
is given by:
A. (E/R)(1 − e−Lt/R )
B. (E/R)e−Lt/R
C. (E/R)(1 + e−Rt/L )
D. (E/R)e−Rt/L
E. (E/R)(1 − e−Rt/L )
ans: E
60. An inductance L, resistance R, and ideal battery of emf E are wired in series. A switch in the
circuit is closed at time 0, at which time the current is zero. At any later time t the emf of the
inductor is given by:
A. E(1 − e−Lt/R )
B. Ee−Lt/R
C. E(1 + e−Rt/L )
D. Ee−Rt/L
E. E(1 − e−Rt/L )
ans: D
61. An inductance L, resistance R, and ideal battery of emf E are wired in series. A switch in the
circuit is closed at time 0, at which time the current is zero. At any later time t the potential
difference across the resistor is given by:
A. E(1 − e−Lt/R )
B. Ee−Lt/R
C. E(1 + e−Rt/L )
D. Ee−Rt/L
E. E(1 − e−Rt/L )
ans: E
62. An 8.0-mH inductor and a 2.0-Ω resistor are wired in series to an ideal battery. A switch in
the circuit is closed at time 0, at which time the current is zero. The current reaches half its
final value at time:
A. 2.8 ms
B. 4.0 ms
C. 3 s
D. 170 s
E. 250 s
ans: A
448
Chapter 30:
INDUCTION AND INDUCTANCE
63. An 8.0-mH inductor and a 2.0-Ω resistor are wired in series to a 20-V ideal battery. A switch in
the circuit is closed at time 0, at which time the current is zero. After a long time the current
in the resistor and the current in the inductor are:
A. 0, 0
B. 10 A, 10 A
C. 2.5 A, 2.5 A
D. 10 A, 2.5 A
E. 10 A, 0
ans: B
64. An 8.0-mH inductor and a 2.0-Ω resistor are wired in series to a 20-V ideal battery. A switch in
the circuit is closed at time 0, at which time the current is zero. Immediately after the switch
is thrown the potential differences across the inductor and resistor are:
A. 0, 20 V
B. 20 V, 0
C. 10 V, 10 V
D. 16 V, 4 V
E. unknown since the rate of change of the current is not given
ans: B
65. An inductor with inductance L resistor with resistance R are wired in series to an ideal battery
with emf E. A switch in the circuit is closed at time 0, at which time the current is zero. A
long time after the switch is thrown the potential differences across the inductor and resistor:
A. 0, E
B. E, 0
C. E/2, E/2
D. (L/R)E, (R/L)E
E. cannot be computed unless the rate of change of the current is given
ans: A
66. If both the resistance and the inductance in an LR series circuit are doubled the new inductive
time constant will be:
A. twice the old
B. four times the old
C. half the old
D. one-fourth the old
E. unchanged
ans: E
Chapter 30:
INDUCTION AND INDUCTANCE
449
67. When the switch S in the circuit shown is closed, the time constant for the growth of current
in R2 is:
..
.....
...
....
...... ...... ......
.
.
.
............................... ..
.................................................. .. .... ... .... ... .... .... ......................
...
..... ........ ........ ........ .....
..
...... ..... ...... ......
...
....
...
...
...
..
...
..
...
...
...
...
..
..
...
.
.
.....
.........
.
....
.
.
...
.........
.
............
......
.
.
.
.
.
.
.
.
.
.
1 .............
2 .............
....
.....
.......
...
...
..
....
...
..
....
...
..
..
...
...
....
...
..
..
..
.
....................................................................................................................................................................................................................
S
L
R
A.
B.
C.
D.
E.
R
L/R1
L/R2
L/(R1 + R2 )
L(R1 + R2 )/(R1 R2 )
(L/R1 + L/R2 )/2
ans: B
68. The diagrams show three circuits with identical batteries, identical inductors, and identical
resistors. Rank them according to the current through the battery just after the switch is
closed, from least to greatest.
.. .. ..
.. .... ... .... ... .... ..
.. .. ..
.......
...
.
............................
..
.
.
.
.
.
.
.
.
.
.
....................
..
..............................
.
...
......
..
...
....
•..... •
A.
B.
C.
D.
E.
450
.. .. ..
.. .... ... .... ... .... ..
.. .. ..
.. .. ..
.........................
.. .. ..
1
..........
......
...........
.....
...........
..
.....
..
...
....
•..... •
2
3, 2, 1
2 and 3 ties, then 1
1, 3, 2
1, 2, 3
3, 1, 2
ans: C
Chapter 30:
INDUCTION AND INDUCTANCE
.. .. ..
.. .... ... .... ... .... ..
.. .. ..
.......
...
.
............................
..
.
.
.
.
.
.
.
.
.
.
....................
..
..............................
.
...
......
..........
......
...........
.....
...........
..
.....
..
...
....
•..... •
3
.......
...
.
............................
..
.
.
.
.
.
.
.
.
.
.
....................
..
..............................
.
...
......
69. Immediately after switch S in the circuit shown is closed, the current through the battery is:
.. .. ..
................................. .......................................................................................................... ..
...
..
.. .. ..
.
...
....
...
..
...
....
...
...
...
........
1
...
...
...
..
...
.
.....................
...........
.
...
......... ..
......
..
..
.
.
.
.
.
.
.
.
.
............
.
.
.
.
.
.
..................
..
2 ...................
..
...
.
................................
.......
...
...
...
...
..
.
...
.
.
.
.
...
.
.
..
....
....
...
....
....
...
...
....
...
..
...
...
.
....
.
.
.
.
.
.
..........................................
........................................................................................................
R
V0
R
L
S
A.
B.
C.
D.
E.
0
V0 /R1
V0 /R2
V0 /(R1 + R2 )
V0 (R1 + R2 )/(R1 R2 )
ans: D
70. A 3.5-mH inductor and a 4.5-mH inductor are connected in series. The equivalent inductance
is:
A. 2.0 mH
B. 0.51 mH
C. 0.13 mH
D. 1.0 mH
E. 8.0 mH
ans: E
71. A 3.5-mH inductor and a 4.5-mH inductor are connected in series and a time varying current
is established in them. When the total emf of the combination is 16 V, the emf of the larger
inductor is:
A. 7.0 V
B. 9.0 V
C. 2.3 V
D. 28 V
E. 36 V
ans: B
72. A 3.5-mH inductor and a 4.5-mH inductor are connected in parallel. The equivalent inductance
is:
A. 2.0 mH
B. 0.51 mH
C. 0.13 mH
D. 1.0 mH
E. 8.0 mH
ans: A
Chapter 30:
INDUCTION AND INDUCTANCE
451
73. A 3.5-mH inductor and a 4.5-mH inductor are connected in parallel. When the total emf of
the combination is 16 V, the rate of change of the current in the larger inductor is:
A. 2.0 × 103 A/s
B. 3.6 × 103 A/s
C. 4.6 × 103 A/s
D. 7.0 × 103 A/s
E. 8.1 × 103 A/s
ans: B
74. An inductor with inductance L and an inductor with inductance 2L are connected in parallel.
When the rate of change of the current in the larger inductor is 1200 A/s the rate of change of
the current in the smaller inductor is:
A. 400 A/s
B. 1200 A/s
C. 1600 A/s
D. 2000 A/s
E. 2400 A/s
ans: E
75. The stored energy in an inductor:
A. depends, in sign, upon the direction of the current
B. depends on the rate of change of current
C. is proportional to the square of the inductance
D. has units J/H
E. none of the above
ans: E
76. An inductance L and a resistance R are connected in series to an ideal battery. A switch in the
circuit is closed at time 0, at which time the current is zero. The energy stored in the inductor
is a maximum:
A. just after the switch is closed
B. at the time t = L/R after the switch is closed
C. at the time t = L/R after the switch is closed
D. at the time t = 2L/R after the switch is closed
E. a long time after the switch is closed
ans: E
77. An inductance L and a resistance R are connected in series to an ideal battery. A switch in
the circuit is closed at time 0, at which time the current is zero. The rate of increase of the
energy stored in the inductor is a maximum:
A. just after the switch is closed
B. at the time t = L/R after the switch is closed
C. at the time t = L/R after the switch is closed
D. at the time t = (L/R) ln 2 after the switch is closed
E. a long time after the switch is closed
ans: D
452
Chapter 30:
INDUCTION AND INDUCTANCE
78. In each of the following operations, energy is expended. The LEAST percentage of returnable
electrical energy will be yielded by:
A. charging a capacitor
B. charging a storage battery
C. sending current through a resistor
D. establishing a current through an inductor
E. moving a conducting rod through a magnetic field
ans: C
79. A current of 10 A in a certain inductor results in a stored energy of 40 J. When the current is
changed to 5 A in the opposite direction, the stored energy changes by:
A. 20 J
B. 30 J
C. 40 J
D. 50 J
E. 60 J
ans: B
80. A 6.0-mH inductor is in a series circuit with a resistor and an ideal battery. At the instant the
current in the circuit is 5.0 A the energy stored in the inductor is:
A. 0
B. 7.5 × 10−2 J
C. 15 × 10−2 J
D. 30 × 10−2 J
E. unknown since the rate of change of the current is not given
ans: B
81. A 6.0-mH inductor is in a circuit. At the instant the current is 5.0 A and its rate of change is
200 A/s, the rate with which the energy stored in the inductor is increasing is:
A. 7.5 × 10−2 W
B. 120 W
C. 240 W
D. 3.0 W
E. 6.0 W
ans: E
82. A 6.0-mH inductor and a 3.0-Ω resistor are wired in series to a 12-V ideal battery. A switch in
the circuit is closed at time 0, at which time the current is zero. 2.0 ms later the energy stored
in the inductor is:
A. 0
B. 2.5 × 10−2 J
C. 1.9 × 10−2 J
D. 3.8 × 10−2 J
E. 9.6 × 10−3 J
ans: C
Chapter 30:
INDUCTION AND INDUCTANCE
453
83. The quantity B 2 /µ0 has units of:
A. J
B. J/H
C. J/m
D. J/m3
E. H/m3
ans: D
84. A 0.20-cm radius cylinder, 3.0 cm long, is wrapped with wire to form an inductor. At the
instant the magnetic field in the interior is 5.0 mT the energy stored in the field is about:
A. 0
B. 3.8 × 10−6 J
C. 7.5 × 10−6 J
D. 7.5 × 10−4 J
E. 9.9 J
ans: B
85. In the diagram, assume that all the magnetic field lines generated by coil 1 pass through coil
2. Coil 1 has 100 turns and coil 2 has 400 turns. Then:
........................................... .......................................... ...
..
...
....
...
...
.
...
.........
...
..
...
.
...
...........................
....... ..
....
.
.
.
.
.
.
..
.
.
.
.
.
.
.
.
...................
....
...
..
...............................
...
..
...
...
.
.
....
.
.
.....
..
....
...
...
.
...
.
.
.
...
....
...
..
...
............................................
...............................................
#1
.............................................................................................
...
...
....
...
...
...
.
.
...
.....
.
...
.
..
....
.................
.
.
.........
.
.
.
.
.
.
.
....
. .
....
.
.... ............
.
...
..
................
.
.
...
..................
...
...
... .............
...
.....
.
..................
..................
...
...
...
........
....
.....
..
...
..
...
..
.
.
..........................................................................................................................
#2
G
S
A.
B.
C.
D.
E.
454
the power supplied to coil 1 is equal to the power delivered by coil 2
the emf around coil 1 will be one-fourth the emf around coil 2
the current in coil 1 will be one-fourth the current in coil 2
the emfs will be the same in the two coils
none of the above
ans: E
Chapter 30:
INDUCTION AND INDUCTANCE
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS
AND ALTERNATING CURRENT
1. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero,
but the capacitor is charged. If T is the period of the resulting oscillations, the next time after
t = 0 that the current is a maximum is:
A. T
B. T /4
C. T /2
D. T
E. 2T
ans: B
2. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero,
but the capacitor is charged. If T is the period of the resulting oscillations, the next time after
t = 0 that the charge on the capacitor is a maximum is:
A. T
B. T /4
C. T /2
D. T
E. 2T
ans: C
3. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero,
but the capacitor is charged. If T is the period of the resulting oscillations, the next time after
t = 0 that the voltage across the inductor is a maximum is:
A. T
B. T /4
C. T /2
D. T
E. 2T
ans: C
4. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero,
but the capacitor is charged. If T is the period of the resulting oscillations, the next time after
t = 0 that the energy stored in the magnetic field of the inductor is a maximum is:
A. T
B. T /4
C. T /2
D. T
E. 2T
ans: B
Chapter 31:
ELECTROMAGNETIC OSCILLATIONS & ALTERNATING CURRENT
455